Geodesic
Monotonicity conditions for a~sequence of generalized polynomials of S.\,N.~Bernshtein and A.\,O.~Gel'fond
Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 747-752.

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It is shown that the sequence of generalized polynomials of S. N. Bernshtein and A. O. Gel'fond, which corresponds to a function $f(x)$, is an increasing or decreasing sequence depending on the concavity or convexity of the function. Analogous results are given in the case of functions of two variables. 
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     author = {V. M. Shakhverdiev},
     title = {Monotonicity conditions for a~sequence of generalized polynomials of {S.\,N.~Bernshtein} and {A.\,O.~Gel'fond}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {747--752},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a12/}
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V. M. Shakhverdiev. Monotonicity conditions for a~sequence of generalized polynomials of S.\,N.~Bernshtein and A.\,O.~Gel'fond. Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 747-752. http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a12/